A triangle has sides 6 cm, 11 cm and cm and its area is 30 cm

MATHEMATICS · Single correct · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

A triangle has sides 6 cm, 11 cm and xx cm and its area is 30 cm2^2. Which of the following equations in xx correctly represents this condition? (a) 17+x2(17+x2−6)(17+x2−11)(17+x2−x)=30\dfrac{17+x}{2}\left(\dfrac{17+x}{2}-6\right)\left(\dfrac{17+x}{2}-11\right)\left(\dfrac{17+x}{2}-x\right)=30 (b) 17+x2(17+x2−6)(17+x2−11)=900\dfrac{17+x}{2}\left(\dfrac{17+x}{2}-6\right)\left(\dfrac{17+x}{2}-11\right)=900 (c) 17+x2(17+x2−6)(17+x2−11)(17+x2−x)=900\dfrac{17+x}{2}\left(\dfrac{17+x}{2}-6\right)\left(\dfrac{17+x}{2}-11\right)\left(\dfrac{17+x}{2}-x\right)=900 (d) (6+11+x)((6+11+x)−6)((6+11+x)−11)((6+11+x)−x)=900(6+11+x)\big((6+11+x)-6\big)\big((6+11+x)-11\big)\big((6+11+x)-x\big)=900

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