Question

The perimeter of a rectangle is 46 meters and its area is 120 sq. m. if so, what will be the length of the diagonal of that rectangle?

A) 15 m
B) 16 m
C) 17 m
D) 20 m

Answer 1

To find the diagonal of a rectangle with a perimeter of 46 meters and an area of 120 square meters, we use the Pythagorean theorem. We first solve for the rectangle's dimensions using the given perimeter and area, finding them to be 15 meters and 8 meters. The diagonal measures 17 meters.

Step-by-step explanation:

To find the length of the diagonal of the rectangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). If we let the length and width of the rectangle be l and w respectively, then the perimeter P is given by P = 2l + 2w, and the area A is given by A = l × w.

Given the perimeter P = 46 meters and the area A = 120 square meters, we can set up two equations:

• 2l + 2w = 46
• l × w = 120

By simplifying the first equation, we get l + w = 23. To express w in terms of l, we rewrite it as w = 23 - l. Now we can substitute w in the second equation:

l × (23 - l) = 120

Solving for l, we get two possible solutions, but only one will make sense in the context of the rectangle's dimensions. Let's assume the solutions are l = 15 and w = 8 (since 15 × 8 = 120, and 15 + 8 = 23).

Then, the diagonal d can be found using the Pythagorean theorem:

d = √(l² + w²)

d = √(15² + 8²)

d = √(225 + 64)

d = √(289)

d = 17 meters

So, the length of the diagonal of the rectangle is 17 meters.