Question

the hypotenuse of a right triangle is25 cm. the difference between the lengths of the other two sides of the triangel is 5cm.find the lengths of sides.

Answer 1

What Are Ratios?

Ratios are used to compare values. They tell us how much of one thing there is compared to another. For example, ratios can be used to compare the number of girl puppies to boy puppies that were born. If we have a total of six puppies, where two are girls and four are boys, we can write that in ratio form as 2:4 (girls:boys). We can also write it in factor form as 2/4. To compare the number of boy puppies to girl puppies, we can simply rewrite our ratio with the number of boys first as 4:2 (boys:girls) or 4/2.

What Are Proportions?

Proportions are related to ratios in that they tell you when two ratios are equal to each other. Let's see how proportions work for our puppies. Our first ratio of girls to boys is 2:4 for our litter of six. If our next litter had a ratio of 4:8 of girls to boys, it would be proportional to our first litter; because if we divide each of our ratios, we will find that they are equal: 2 / 4 = 0.5 and 4 / 8 = 0.5, as well. My ratios are proportional if they divide into the same number.

When things are proportional, they are also similar to each other, meaning that the only difference is the size. For our two litters of 

Answer 2

Given , hypotenuse = 25cm

Let x cm and (x+5)cm be the length of other two sides.

Now, by applying pythagoras theorem,

25 × 25 = x2 + (x+5)2
=> 625 = x2 + x2 + 2.x.5 + 25
=> 625 = 2x2 + 10x + 25
=> 2x2 + 10x + 25 - 625 = 0
=> 2x2 + 10x - 600 = 0
=> 2 ( x2 + 5x - 300 ) = 0
=> x2 + (20-15)x - 300 = 0
=> x2 + 20x - 15x - 300 = 0
=> x ( x + 20 ) - 15 ( x + 20) = 0
=> (x+20) (x-15) = 0

Either, x + 20 = 0 i.e. x = -20 is neglected
Or, x - 15 = 0 i.e. x = 15

Therefore, the lengths of the sides are 15cm and x+5 = 15+5 = 20cm