The diagonal of a rectangle is 25m long and 1 side is 5m longer than the other side.?

Question

I am supposed to find the dimensions of the rectangle. I already have the dimensions (15m by 20m) but I don't know how to get there. (A mathematician I am not.) Thanks

Answer 1

base = x +5
height = x

Based on Pythagorean Theorem

a^2 + b^2 = c^2

x^2 + x^2 + 10x + 25 = 25^2
2x^2 + 10x = 600
x^2 + 5x - 300 = 0
x= -20, 15
Since x cannot be negative

x=15, x+5=20

Answer 2

Let one side of the rectangle be x m,and the other side =x+5 m
The diagonal of a rectangle forms a right angled triangle with the other two sides of the rectangle,the diagonal being the hypotenuse
Therefore, 25^2=x^2+(x+5)^2[ according to Pythgoras theorem]
=>625=x^2+x^2+10x+25
=>2x^2+10x+25-625=0
=>2x^2+10x-600=0
=>x^2+5x-300=0
=>x^2+20x-15x-300=0
=>x(x+20)-15(x+20)=0
=>(x+20)(x-15)=0
Rejecting the negative value of x,we get
x=15m
Therefore ,one side of the rectangle is 15 m and the other side is 15+5 or 20 m

Answer 3

The fact that D = 25 m is given is a strong hint that it should be used.

So, here's what we know: D = 25 and L = W + 5; where L is the long side and W is the width or short side.

From the Pythagorian equation, we also know that D^2 = W^2 + L^2 = W^2 + (W + 5)^2 = W^2 + W^2 + 10W + 25 = 2W^2 + 10W + 25 = 625; so that 2W^2 + 10W = 600 or W^2 + 5W - 300 = 0

If you solve for W, you'll find W = 15; you can use the quadratic equation formula to solve for W.

Once you have W, just plug that into L = W + 5 to find the long side.

Answer 4

Let the sides be a & b
One side is 5m longer than other => a = 5b
diagonal of a rectangle is sqrt(a^2+b^2)
= sqrt [(b+5)^2+b^2] which is equal to 25

=> b^2+10b+25+b^2 = 25^2
b = 15 and b = -20 are the roots of the equation, but since side cannot be negative we take b = 15

so one side of rect is 15 m other side is 5m longer than that which makes the other side 20 m

Answer 5

letting the shorter side be 'x'

by pythagoros therom,
x^2 + (x+5)^2 = 25^2
2x^2 + 10x + 25 = 625
x^2 + 5x - 300 = 0
(x+20)(x-15)=0

therefore x=15m, rejecting the negative answer of -20

Answer 6

suppose the length of the shorter side is 'x'
then longer side is 'x' + 5, right?
now consider the 2 sides and the diagonal, together they constitute a right triangle.
so use pythagoras theorem
ie.., 'x'squared + ('x'+5) squared = 25 squared.
solve for 'x'!!!