Four more than three-fifths of a number is thirteen what number is it

Hello from MrBillDoesMath!

15

Discussion.

Call the number referred to "n".  Then the problem statement becomes:

4 + (3/5) * n = 13

Multiply both sides of the equation by 5 :

5 ( 4 + (3/5)*n) = 13 * 5  or

5*4 + 5 * (3/5)**n = 13*5

Cancelling the boldfaced 5's gives:

5*4 + 3*n = 13 *5  or

20 + 3*n = 65

Subtracting 20 from both sides gives:

3*n = 65-20 - 45

Dividing by 3 gives n = 15

Check: 4 + (3/5)*15 =  4 + 9 = 13!   Bingo

Regards, MrB

1000

Step-by-step explanation:

Given: Dimensions of each triangular piece used in umbrella.

Reasoning: By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and

s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2

We know that umbrella is made of 10 triangular pieces of cloth of two different colours.

Let us calculate the area of one triangle.

For each triangle, a = b = 50 cm, c = 20 cm

Semi Perimeter

s = (a + b + c)/2

= (50 + 50 + 20)/2

= 120/2

= 60 cm

By using Heron’s formula,

Area of triangle = √s(s - a)(s - b)(s - c)

= √s(s - a)(s - b)(s - c)

= √60(60 - 50)(60 - 50)(60 - 20)

= √60 × 10 × 10 × 40

= 200√6 cm2

Therefore,

Area of 10 triangular pieces = 10 × 200√6 cm2 = 2000√6 cm2

Hence, cloth required for each colour = (Total area of the cloth)/2

= (2000√6)/2

= 1000√6 cm2

Thus, 1000√6 cm2 cloth of each colour is required for the umbrella