Chapter 11: Q. 80 (page 774)

An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.

Short Answer

Expert verified

The sides of the squares are $6 f e e t a n d 4 f e e t$ .

Step by step solution

Step 1. Given information.

Assume the sides of the two squares are x,y.

From the question,

$x^{2} + y^{2} = 52 . . . . . . (i) \frac{x}{y} = \frac{2}{3} . . . . . . (i i)$

Solve equation (ii) for x,

$x = \frac{2}{3} y$

Substitute the value of xin equation (i),

localid="1646843569274" ${(\frac{2}{3} y)}^{2} + y^{2} = 52 \frac{4}{9} y^{2} + y^{2} = 52 \frac{4 y^{2} + 9 y^{2}}{9} = 52$

Step 2. Find the value of x.

Continuing the above equation,

$\frac{13 y^{2}}{9} = 52 y^{2} = \frac{52}{13} \times 9 y^{2} = 36 y = \pm 6$

Negative value of the side of the square is not considered as length cannot be negative.

Substitute localid="1646843695159" $y = 6$ in equation (ii),

localid="1646843717935" $\frac{x}{6} = \frac{2}{3} x = \frac{2}{3} \times 6 x = 4$

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An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of x.

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An area of 52feet2is to be enclosed by two squares whose sides are in the ratio of2:3. Find the sides of the squares.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Calculus

Geometry

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.