Question

Find the area of rectangle one side of which measures 12m and the diagonal is 13m

Answer 1

Answer:

60 sq m

Step-by-step explanation:

let ABCD be the rectangle

opposite side of rectangle are equal

each angle is 90°

sides are AB, BC, CD, AD

diagonals are AC, BD

AB = 12 m

AC = 13 m

ABC is a right angle triangle with base AB and hypotenuse AC

using Pythagoras theorem

${ac}^{2} = {ab}^{2} + {bc}^{2} \\ {13}^{2} = {12}^{2} + {bc}^{2} \\ {bc}^{2} = {13}^{2} - {12}^{2} \\ {bc}^{2} = 169 - 144 \\ {bc}^{2} = 25 \\ bc = \sqrt{25} \\ bc = 5m$

the side BC = 5 m

area of rectangle ABCD = base (AB) × height (BC)

= 12 × 5

= 60 sq m

hope you get your answer