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Answer on Geometry Question for Shaderica

Question #5676
What is the measurement of AB?
abc is an isosceles triangle with ab = ac and a median (bd)
the perimter of abc is 60 units .
what is the measurment of segment ab
Expert's answer
We suppose that AB=AC=BD(median), because if not then there is no use for BD, and the information is not sufficient
<img style="width: 309px; height: 195px;" src="data:image/png;base64,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" alt="">
1) AB=AC=BD=x
2) BD is a median ⟹ according to the definition of the median, AD=DC=x/2 (Look at the image1)
3) Let’s construct a BH –an altitude in the triangle ABD. According to the definition of the altitude BH is perpendicular to the vertex AD n to the vertex AC, because AC includes AD. (Look at the image1). So angle ∠BHA=∠BHD=90˚ and we get two right triangles – BHA and BHC.
4)ABD is an isosceles triangle, because AB=AD=x. In the isosceles triangle altitude BH is also a median of the triangle ABD ⟹ AH =HD =(x/2)/2=x/4.
5) Theorem by Pythagoras defines the relationship between the three sides of a right triangle: , where& is the length of the hypotenuse and , are the lengths of the other two sides.
6) According to this theorem, use it to the triangle AHB(where AB=x and AH=x/4) then we can find
<img style="width: 247px; height: 30px;" src="data:image/png;base64,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" alt="">
7) According to this theorem, use it to the triangle BHC(where HC=HD +DC = x/4 + x/2 =3/4x and
lt;img style="width: 88px; height: 27px;" src="data:image/png;base64,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" alt="">
& then we can find
<img style="width: 258px; height: 30px;" src="data:image/png;base64,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" alt="">
8) So
<img style="width: 86px; height: 53px;" src="data:image/png;base64,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" alt="">
9) The& perimeter of ABC is 60 units, so
<img style="width: 261px; height: 40px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAY4AAAA9CAIAAAA1TxlEAAAGtklEQVR4nO2d0YHCIBBErcuCUo/VpBmL8T7iaQgLzC5LCDjv04tsGGBkgeRuL0IIuTy33jdACCFlaFVkPp6P+w2h931OSSvx2VpkPp6P++3+ePa+jd+klfi0KjIf63K7LWvvu/hRWolPqyLT8XzcaVW9aCY+rYpMB/O/jjQTn1ZFpmNdbrSqXjQTn1ZFpoNLVR1pJj6tiswG87+OtBOfVkVmg/lfR9qJT6sisxGnIOuyP3vI3LAh7cSnVZHJOO6Wb6en/z/YBg7dqhENxadVkck4rpY8H/f96FgXWlU7GopPqyKTkd+Cej7uXMlqR0PxaVVkLnKnpelTjWkpPq2KzIW8W75b22Xy146W4tOqyFzkd8u3ZV5OrBrRUnxaFZmL0mnpcE+KuNJSfFoVmYo4BVmXYGwMblXrcuFZoVZ81fIVrYpMRZyChBvklx7qRS7us2rxNfVJWNXxpaNRYYcL6sT7FFYqJnoXakWfKwUND9lWxdMW5VnNX0NIQVz7alfkkR12r559xSA+/tMhWFVxYCVenmzuArvyCkcyRGxxi0FFGWx9QVGUdzV/janfqhc7VaK7dLIrk/iwVx2tKjHXWNf1eMW39PgTFe8GWHKH7j+DPfx7QhsgBS4HFR4C+L8L8fpMULgoXTXPp8W5JN8yZ36rgjCnijKubBeVyvMUyyQ+vC14sKp3TTMVla8of69wq8uaeUBIW3q5DeCgYj0drEr6sELEk7i+VU38qipwTG+9CBHUvTVt4qPrVaFVlR8nTOmFCyQVuH3PrexiGwBBz7cqs4RaREuEniSFO7cihOuAqZ9/flOqlr8iliYAn/XFDy95W5VVfLBigVUBtUwV+27hZX3tW1vgUHqQqcrx9UO41AZAUKmm73olClZZlVCUyak0Ukc3tLsjzTDAbhEO4W5VFWWty/btsE8k0vIwqrYV1E2AWhD+9oIWVmUpDqxZYFWfWh7Wgb/13jtSyE4hRcsd1tSkmzYccS20ARD09TpqUOitgFXli7Kd5DVa1WGkwL1b1bnBEK4DxuvFbt+kBLk9WysomwBrpPQATVzraFVm8bGqCVaVExyyKuU9xsuCwSfYGM72FmH6Ugj6yonxuRINChR1/hMfn1lcvuUUwsIhasosV8olS3sP47XpKj3YBPuL89cUjaqd8q8K8e1WJc1qwgmTk1VJb6+JyvG2Kiho4rPDXqfOqrJF9Xg4DXqKtK5zyyGaDZg4BcnFyf4vcs1Wmh38QV5gugQsqLW0Krv4ZqtKHPfc7gJZq0LJTOLi5WZNybmZLRg0GTa5pKRdVj8WZZqW1gEfvQ2+oM/FsyE80xCv/O912rlwvAmgRXe3YWLALr7ZqqJwe6tCdumw1L1g8Mj6WIp0G8BB0/oZloehoixmb1+rOn4XC6vt3EgIb6vyy/9gXcytoGmC3Hi2bVA2sCqb+AarSnwncDDZzoJPoZZLJzzRmA1SUIRkGyiCIlNMLChalLqarxqr+gZXbD3qOjcWwnHA1B9V2NgGnbiCmY6rbwVdExRO1VgPNLlZlV18yw6gtFoVDaA4iT8uu9TeXso24i8kxE61gSpo5jCU2CS2c1U11awgrC1sVpobQUM4W5W9pHV7CcB3LRP3KgvqJsj1IrtFuFpVy/wv/WBNiLCKk72kRMFIhYZDdtGC0hMfw0E1ATNBlUVpo5pI/RYUQ+CdGw/hOGCq8r9vzxcm/s/H3WO6FkXTNIHQfXMLr2VJfa3KLD66oSRtgiRPVR2LNw+j4t3J7Rb7qNdETggqd4OKcyNwUXXVLCIuir0/dF2TbhoiFdVsKNL2d2qaW4tNn3ilP5d5nrqZXCE+vPXN91WRWajL/wagwyYxjFl8OM2mVZFZSO+Wh7OPa451hJNOUFiwio8vCNKqyCwkVkvCuciVZyZlrutVNvE19aFVkUlIpSCHQdR2X685F719m/gq56VVkcHIjQpgDEsPVhGUjuLTqsg4ZB+Zw3bL6VRWeotPqyJj8Pk9Fx+qx7ag/M/S/ghXEJ9WRYZDPKJdHC3XXZIeim7i06rIeEiPSxZSECZ+XvQSn1ZFRiRKRLKnpS+6bTYqfcSnVZEhOf62Z1KQ6Dd9XTi/qqKL+LQqMijhM3PJFER8To4zrEo6iE+rIsOyT0Tc3qpHME4Xn1ZFxuWbiEz/qPL1OFt8WhUZmf9E5M4DU+dzrvi0KjI230PUzP9O50zxaVVkcCzvyyZOnCg+rYoMD/wiSeLPaeLTqsgEcP+vIyeJT6sihAwArYoQMgC0KkLIANCqCCEDQKsihAwArYoQMgB/PoSdr41tcOUAAAAASUVORK5CYII=" alt="">
10) From that we can find
<img style="width: 153px; height: 52px;" src="data:image/png;base64,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" alt="">
The answer is :&
<img style="width: 115px; height: 51px;" src="data:image/png;base64,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" alt="">

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