Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The height of a triangle is equal to the perimeter of a square whose diagonal is $8 \sqrt{2}$ metre and the base of the same triangle is equal to the side of a square whose area is 729sq. metre. What is the area of the triangle? (In sq. metre) [United India Insurance (UIICL) Assistant (Online) Exam, 2015]
(a)378
(b)206
(c)472
(d)432
Answer
Answer (as printed): D
Explanation
Height of triangle = perimeter of square Diagonal of square $=8 \sqrt{2} \mathrm{m}$ $$\text { ∴ Length of each side of square }=\frac{8 \sqrt{2}}{\sqrt{2}}=8 \mathrm{m}$$ ∴ Perimeter of square $=4 \times 8=32 \mathrm{m}=$ Height Area of other square $=729$ Side of square $=\sqrt{729}$ $$\text { = } 27 \text { m = base of triangle }$$ ∴ Area of triangle $$\begin{aligned} & =\frac{1}{2} \times \text { base × height } \\ & =\frac{1}{2} \times 27 \times 32=432 \text { sq. m. } \end{aligned}$$