Question

REFER TO PHOTO, WILL GIVE 90 POINTS

Answer 1

• RS = 7cm .

Explanation:

To find:-

• The value of RS .

Answer:-

Let us take that, PQ = s , QS = p , QR = a and RS = b.

Here we can see that, ∆PQR and ∆PQS are right angled triangles .

Here, the value of RS would be,

`\longrightarrow b = p - a \\`

Finding the value of "p" :-

In ∆PQS ,

`\longrightarrow \tan 45^o =(perpendicular)/(base) \\`

`\longrightarrow 1 = (72cm)/(p)\\`

`\longrightarrow \large \pmb { p = 72cm }\\`

Finding the value of "a" :-

In ∆PQR , we can use Pythagoras theorem .

• According to which, in a right angled triangle, the sum of squares of base and perpendicular is equal to the square of hypotenuse.
• Hypotenuse is the longest side of the triangle and the side opposite to 90° is hypotenuse.

So that,

`\longrightarrow\Large \pmb{\boxed{ p^2 + b^2 = h^2 }}\\`

where the symbols have their usual meaning.

On substituting the respective values, we have;

`\longrightarrow 72^2 + a^2 = 97^2 \\`

`\longrightarrow a^2 = 97^2-72^2 \\`

`\longrightarrow a^2 = 9409 - 5184 \\`

`\longrightarrow a^2 = 4225 \\`

`\longrightarrow a =√(4225)\\`

`\longrightarrow \large\pmb{ a = 65\ cm } \\`

Hence we can find the value of b as ,

`\longrightarrow b = p-a \\`

`\longrightarrow b = 72cm - 65cm\\`

`\longrightarrow b = 7cm \\`

`\longrightarrow\large\pmb{\underline{\boxed{\pmb{ \overline{RS} = 7cm }}}}\\`

Therefore the value of RS is 7cm .