One side of a right-angled triangle is 10 cm, and its hypotenuse is 5 cm longer than the other side. What is the length of the other side?
Answer and explanation
Correct answer: 7.5 cm
Let the other side be \(x\) cm. Then the hypotenuse is \((x+5)\) cm. By the Pythagorean theorem, \(x^2+10^2=(x+5)^2\), so \(x^2+100=x^2+10x+25\). Hence, \(10x=75\) and \(x=7.5\) cm. Therefore, option D is correct. Exam tip: in a right triangle, the hypotenuse is the longest side, so it must be represented by \(x+5\), not by \(x\).
Frequently asked questions
What is the correct answer to this question?
7.5 cm
Why is this the correct answer?
Let the other side be \(x\) cm. Then the hypotenuse is \((x+5)\) cm. By the Pythagorean theorem, \(x^2+10^2=(x+5)^2\), so \(x^2+100=x^2+10x+25\). Hence, \(10x=75\) and \(x=7.5\) cm. Therefore, option D is correct. Exam tip: in a right triangle, the hypotenuse is the longest side, so it must be represented by \(x+5\), not by \(x\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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