Question

A rectangle made of square tiles measures 10 tiles long and 8 tiles wide.
What is the width of a similar rectangle whose length is 15 tiles?​

Answer 1

Answer:

12 tiles

Step-by-step explanation:

Let,

• The rectangle with dimensions "10 tiles and 8 tiles" be known as "s".
• The rectangle with dimension "15 tiles" be known as "l"

Since the length of the larger rectangle is similar to the smaller rectangle, we can compare the dimensions of both rectangles by forming a ratio.

$\text{(L of "s")}:\text{(B of "s")}= \text{(L of "l")}: \text{(B of "l")}$

Let,

• ⇒ Length of "s" be L₁
• ⇒ Breadth of "s" be B₁
• ⇒ Length of "l" be L₂
• ⇒ Breadth of "l" be B₂

$\implies \text{L}_{1} }:\text{B}_{1} = \text{L}_{2} : \text{B}_{2}$

We are already given:

• Length of "s"     =   L₁   =   10 tiles
• Breadth of "s"   =   B₁   =   8 tiles
• Length of "L"    =   L₂   =   15 tiles

$\implies 10:8 = 15 : \text{B}_{2}$

To simplify the ratio, multiply the extremes together and take them on one side. Then, multiply the middles together and take them on the other side.

$\implies 10 (\text{B}_{2}) = 15(8)$

Divide 10 both sides to obtain the width of the larger rectangle.

$\implies \dfrac{10 (\text{B}_{2}) }{10} = \dfrac{15(8)}{10}$

Simplify the equation as necessary.

$\implies \text{B}_{2} = 12$

Thus, the width of the larger rectangle is 12 tiles.