word problem, Eqation, Set up an equation

Question

Set up an equation and solve the following problem.The combined area of two squares is 10 square meters. The sides of the larger square are three times as long as the sides of the smaller square. Find the dimensions of each of the squares.

 

dimensions of a smaller square  __________m X ______________m

 

dimensions of a larger square   ___________m X ______________m

Answer 1

Let's say

 

dimensions of smaller square =  A and A 

(length and width are equal for a square)

 

dimensions of larger square = B and B

 

combined are of both squares are then

 

A² + B² = 10 m²

 

We are also given: 

The sides of the larger square are three times as long as the sides of the smaller square

 

B = 3A

 

Substitute this in for B in the first expression

 

A² + (3A)² = 10 m²

 

A² + 9A² = 10 m²

 

10A² = 10 m²

 

A² = 1 m²

 

A = 1 m

 

Then the sides of the larger square, B = 3(1 m) = 3 m

 

(1m)(1m) + (3m)(3m) = 10 m²

 

Small square is 1m x 1m

Large square is 3m x 3m

 

Answer 2

Nathan, how do we find the area of a square? One side squared, right?

 

Let a = a side of the smaller square. Then the area is a².

 

Then a side of the larger square is 3a and the area is 9a².

 

a² + 9a² = 10

10a² = 10

a² = 1

a = 1

 

So, the smaller square is 1 x 1 and the larger is 3 x 3.