The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides ?

byAmlesh Mahato •February 28, 2021

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Solution:

⇨Let the base of the right angle triangle be x cm

⇨Than Altitude/Perpendicular is = x-7 cm

⇨Given, Hypotenuse is = 13 cm

From Pythagoras Formula

$The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides ?$

$\large \Rightarrow (13)^2=x^2+(x-7)^2$

$\large \Rightarrow 169=x^2+x^2-2.x.7+7^2$

$\large \Rightarrow 169=2x^2-2.x.7+49$

$\large \Rightarrow 169=2x^2-14x+49$

$\large \Rightarrow 2x^2-14x+49-169=0$

$\large \Rightarrow 2x^2-14x-120=0$

$\large \Rightarrow x^2-7x-60=0$

$\large \Rightarrow x^2-(12-5)x-60=0$

$\large \Rightarrow x^2-12x+5x-60=0$

$\large \Rightarrow x(x-12)+5(x-12)=0$

$\large \Rightarrow (x+5)(x-12)=0$

$\large \Rightarrow x+5=0,x-12=0$

$\large \Rightarrow x=-5,x=12$

⇨x=-5, Length can not be negative, Hence it rejected.

⇨Therefore Length of the Base = 12 cm

⇨Length of Altitude/ Perpendicular = x-7 = 12-7 = 5 cm

Exercise 4.2

1. Find the roots of the following quadratic equations by factorisation:

(i) $x^2-3x-10=0$

(ii) $Find the roots of 2x^2+x-6=0 quadratic equations by factorization ?$

(iii) $Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$

(iv) $Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

(v) $\large 100x^{2}-20x+1=0$

3. Find two numbers whose sum is 27 and product is 182.

4. Find two consecutive positive integers, sum of whose squares is 365.

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ` 90, find the number of articles produced and the cost of each article.

Tags: Chapter-4 Exercise-4.2 Math- Class 10

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