Question

the altitude of a right angle triangle is 7 cm less than its base if the hypotenuse is 13 cm find the other two side​

Answer 1

Answer:

12,5

Step-by-step explanation:

              let the altitude be 'a' and the base be 'b' and the hypotenuse be 'h'

                        then by given condition,

                            a=b-7 and h=13

      we know that by pythagores theorem,

                                h^2=a^2+b^2

                                (13)^2=(b-7)^2+b^2

                                169=b^2+49-14b+b^2

                                 2b^2-14b+49-169=0

                                    2b^2-14b-120=0

                                      b^2-7b-60=0

                                      b^2-12b+5b-60=0

                                       b(b-12)+5(b-12)=0

                                       (b-5)(b-12)=0

                                          b=5 or b=12

if b=12 then a=12-7=5 but 'b' can't be 5 because if b=5 then 'a' become negative so sides are 12,5

Answer 2

Given,

• Altitude of right triangle is 7 cm less than its base.
• Hypotenuse is 13 cm.

To find,

• The other two sides.

Solution,

• Let x be the base of the triangle
• Then altitude will be (x-7)

We know that,

$\sf{Base^2+Altitude^2=Hypotenuse^2}$

So, by pythagoras theorem,

${x}^{2} + ( {x - 7)}^{2} = {13}^{2} \\ \\ ⟹2 {x}^{2} - 14x + 49 = 169 \\ \\ ⟹2 {x}^{2} - 14x + 49 - 169 = 0 \\ \\ ⟹2 {x}^{2} - 14x - 120 = 0 \\ \\ ⟹2( {x}^{2} - 7x - 60) = 0 \\ \\ ⟹ {x}^{2} - 7x - 60 = \frac{0}{2} \\ \\⟹ {x }^{2} - 7x - 60 = 0 \\ \\ ⟹ {x}^{2} - 12x + 5x - 60 = 0 \\ \\ ⟹x(x - 12) + 5(x - 12) = 0 \\ \\ ⟹(x - 12)(x + 5) = 0$

So, x = 12 or x = -5

Since,the side of a triangle cannot be negative,so the base of the triangle is 12 cm.

And the altitude will be (12-7) = 5 cm