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8.Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.

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Let's denote the lengths of the adjacent sides of the rectangle as 5x5x and 12x12x, where xx is a positive constant. The perimeter (PP) of the rectangle is given by the sum of all its sides: P=2(5x+12x)P=2(5x+12x) Now, substitute in the values we have: 34=2(17x)34=2(17x) Now, solve for xx: 17x=1717x=17 x=1x=1 Now...
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Let's denote the lengths of the adjacent sides of the rectangle as 5x5x and 12x12x, where xx is a positive constant. The perimeter (PP) of the rectangle is given by the sum of all its sides: P=2(5x+12x)P=2(5x+12x) Now, substitute in the values we have: 34=2(17x)34=2(17x) Now, solve for xx: 17x=1717x=17 x=1x=1 Now that we have the value of xx, we can find the lengths of the adjacent sides: Length of one side = 5x=5×1=55x=5×1=5 cm Length of the other side = 12x=12×1=1212x=12×1=12 cm Now, we can use the Pythagorean theorem to find the length of the diagonal (dd) of the rectangle: d2=(5)2+(12)2d2=(5)2+(12)2 d2=25+144d2=25+144 d2=169d2=169 d=169d=169 d=13d=13 So, the length of the diagonal of the rectangle is 13 cm. read less
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