Question

(1 Find two numbers whose sum is 27 and product is 182.
(2 The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm, find the other two sides.
(3 Solve the problems given in Example 1.

Answer 1

Answer:

• Let x and y be two numbers

Given, x+y=27                    ............(1)

and xy=182                            .............(2)

From (1), we get x=27−y

Put x=27−y in (2) we get,

(27−y)y=182⇒27y−y2=182⇒y2−27y+182=0

⇒(y−14)(y−13)=0

⇒y=14 or y=13

∴ if y=14 then x=13 and if y=13 then x=14

Two numbers are 13 and 14

• Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

x2+(x−7)2=(13)2

2x2−14x+49−169=0

2x2−14x−120=0

x2−7x−60=0

x2−12x+5x−60=0

(x−12)(x+5)=0

x=12,x=−5

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.

Hope this helps you

Please mark as brainliest