The area of a triangular lawn is 1600 , m^{2} | vedclass

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Question

(B) Let the length of each equal side be $x \, m$.The sides of the triangle are $x, x,$ and $64$.The semi-perimeter $s = \frac{x + x + 64}{2} = x + 32

Vedclass · Accepted Answer

$59.36$

Vedclass · Answer

(B) Let the length of each equal side be $x \, m$.The sides of the triangle are $x, x,$ and $64$.The semi-perimeter $s = \frac{x + x + 64}{2} = x + 32$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.$1600 = \sqrt{(x+32)(x+32-x)(x+32-x)(x+32-64)}$.$1600 = \sqrt{(x+32)(32)(32)(x-32)}$.$1600 = 32 \sqrt{(x+32)(x-32)}$.$50 = \sqrt{x^{2} - 32^{2}}$.Squaring both sides,$2500 = x^{2} - 1024$.$x^{2} = 3524$.$x = \sqrt{3524} \approx 59.36 \, m$.

The area of a triangular lawn is $1600 \, m^{2}$. If one side is $64 \, m$ long and the other two sides are equal in length,the length of each equal side is......$m$

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