The area of a rectangle and the square of its perimeter are in the ratio 1 ∶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio ?

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1 : 4 — Easy Write area and the squared perimeter in terms of the sides $l$ and $b$, form the ratio, and reduce it to a single equation in the ratio $l:b$. Solve the resulting quadratic. 1 Set up the ratio. Area $=lb$, perimeter $=2(l+b)$, so its square is $4(l+b)^2$. $$\begin{aligned} &\frac{lb}{\big[2(l+b)\big]^2}=\frac{1}{25}\ &\Rightarrow\ 25\,lb=4(l+b)^2 \end{aligned}$$ 2 Introduce the side ratio. Let $t=\dfrac{l}{b}$ and divide through by $b^2$. $$\begin{aligned} &25t=4(t+1)^2\ &\Rightarrow\ 4t^

CAT 2018 Slot 2 — QA Question 18

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