Question

1. examine the rectangle shown below. find its perimeter and area. 6 mm 15 mm

Explanation:

Step1: Find the other side of the rectangle using Pythagorean theorem

Let the length of the unknown side be $x$. In a right - triangle formed by the sides of the rectangle and the diagonal, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 15$ (diagonal) and $a = 6$ (one side). So $x=\sqrt{15^{2}-6^{2}}=\sqrt{225 - 36}=\sqrt{189}=3\sqrt{21}\approx13.75$ mm.

Step2: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$. Here $l=13.75$ mm and $w = 6$ mm. So $P=2(13.75 + 6)=2\times19.75 = 39.5$ mm.

Step3: Calculate the area of the rectangle

The area formula of a rectangle is $A=l\times w$. So $A=13.75\times6 = 82.5$ $mm^{2}$.

Answer:

Perimeter: $39.5$ mm, Area: $82.5$ $mm^{2}$