1. Construct the Isosceles triangle from given data below : Altitude = 55mm Perimeter = 135mm

  base: 22 37/54; sides: 56 17/108

Step-by-step explanation:

If we let x represent half the length of the base, and y represent the length of the side, then we have ...

  2x +2y = 135 . . . . . perimeter relation

  x^2 +55^2 = y^2 . . . . Pythagorean theorem relation

Solving for y and substituting into the second equation, we have ...

  y = 135/2 -x

  x^2 + 3025 = (67.5 -x)^2

  3025 = -135x +4556.25 . . . . . . expand, subtract x^2

  135x = 1531.25 . . . . . . . . . . add 135x -3025

  x = 1531.25/135 = 11 37/108

The length of the base is double this value, 22 37/54.

The length of each side is 67.5 -11 37/108 = 56 17/108.

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Check

The perimeter is the base plus two side lengths:

  22 37/54 + 2(56 17/108) = (22 +112) +37/54 +17/54 = 134 +1 = 135.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.