Question

please solve it.. fast

Answer 1

Answer:

Step-by-step explanation:

Let one of the sides be x;

other side =x-7;

hypotenuse=13

By pythogoras theoram

13^2=x^2+(x-7)^2;

169=2x^2+49-14x;

2x^2-14x-120=0

x^2-7x-60=0

x^2-12x+5x-60=0;

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

(x+5)(x-12)=0;

x=12cm

x-7=12-7=5cm

Answer 2

ANSWER

Let base of right angled triangle be x.

Then, altitude = x - 7

Hypotenuse = 13cm

By Pythagoras Theorem,

(Hypotenuse)^2 = (base)^2 + (altitude)^2

$= > ({13})^{2} = ({x})^{2} + ({x - 7})^{2}$

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

x = 12cm or x = -5cm

base cannot be negative.
so,
base = 12cm

Altitude = 12-7
= 5cm



HOPE IT HELPS
THANKS