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Chapter 11: Q. 80 (page 774)

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

Expert verified

The sides of the squares are 6feetand4feet.

Step by step solution

01

Step 1. Given information.

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

From the question,

x2+y2=52......(i)xy=23......(ii)

Solve equation (ii) for x,

x=23y

Substitute the value of xin equation (i),

localid="1646843569274" 23y2+y2=5249y2+y2=524y2+9y29=52

02

Step 2. Find the value of x.

Continuing the above equation,

13y29=52y2=5213脳9y2=36y=卤6

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

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

localid="1646843717935" x6=23x=23脳6x=4

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